Bài tập CALCULUS 11

Created by T Madas Question 42 (***) A curve C has the following equation f ( x ) = 4x x − 25 x , x≥0 16 a) Find a simplified expression for f ′ ( x ) b) Determine an equation of the tangent to the curve at the point where x = , giving the answer in the form ax + by = c , where a , b and c are integers C1I , f ′ ( x ) = x − 25 x , x + y = 18 Question 43 (***) The curve C has equation y = x3 − x + 12 x − Find the coordinates of the stationary point of C and use a clear method to determine its nature C2M , point of inflexion at Created by T Madas ( 2,3) Created by T Madas Question 44 (***) f ( x) = ( x 3x − x ) , x >0 Show clearly that  f ( x ) dx = P x + Qx + C , where P and Q are integers to be found, and C is an arbitrary constant P = −20 , Q = Question 45 (***) The point P ( 3,0 ) lies on the curve C whose gradient function is given by dy = x − 14 x + 12 dx a) Find an equation of the tangent to C at the point P The point Q lies on C , so that the tangent at Q is parallel to the tangent at P b) Find the x coordinate of Q y = − 3x , x = Created by T Madas Created by T Madas Question 46 (***) y y = −4 x + 24 x − 20 x O A B y = x − 6x + The figure above shows the graph of the curves with equations y = −4 x + 24 x − 20 and y = x2 − x + The two curves intersect each other at the points A and B The finite region R bounded by the two curves is shown shaded in the figure Find the exact area of R SYN-D , 160 Created by T Madas